Problem: What's the first wrong statement in the proof below that $ \triangle BDE \cong \triangle BCE$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \angle DBE \cong \angle ABC$ $, \ $ $ \angle BDE \cong \angle ACB$ $, \ $ $ \overline{DE} \cong \overline{AC}$ $, \ $ $ \overline{BE} \cong \overline{EF}$ $, \ $ $ \angle DBE \cong \angle CFE$ $, \ $ and $\ $ $ \overline{BD} \cong \overline{CF}$ Proof $ \triangle FCE \cong \triangle BDE$ because SAS $ \overline{CE} \cong \overline{DE}$ because corresponding parts of congruent triangles are congruent $ \triangle BCA \cong \triangle BDE$ because AAS $ \overline{BC} \cong \overline{BD}$ because corresponding parts of congruent triangles are congruent $ \triangle BCE \cong \triangle BDE$ because SSS
Solution: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. There is no wrong statement in this proof.